Class 12 Continuity And Differentiability · Long Answer3 Marksimplicit_differentiation
Class 12 Maths · Continuity And Differentiability · Long Answer #79
If x sin(a+y)+sin a cos(a+y)=0, prove y′=sin²(a+y)/sin a where sin a≠0 and sin(a+y)≠0.
✅ Step-by-Step Solution
Final Answer: sin²(a+y)/sin a
- Divide the relation by sin(a+y): x=−sin a cot(a+y).
- Differentiate with respect to y: dx/dy=sin a cosec²(a+y).
- This is nonzero under the stated assumptions, so invert it: dy/dx=1/[sin a cosec²(a+y)].
- Therefore y′=sin²(a+y)/sin a.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Divide the relation by sin(a+y): x=−sin a cot(a+y).
- [1 mark] Differentiate with respect to y: dx/dy=sin a cosec²(a+y).
- [1 mark] This is nonzero under the stated assumptions, so invert it: dy/dx=1/[sin a cosec²(a+y)].
- [0.5 marks] Therefore y′=sin²(a+y)/sin a.
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